Model for Thermal Relic Dark Matter of Strongly Interacting Massive Particles

A recent proposal is that dark matter could be a thermal relic of $3\to 2$ scatterings in a strongly coupled hidden sector. We present explicit classes of strongly coupled gauge theories that admit this behavior. These are QCD-like theories of dynamical chiral symmetry breaking, where the pions play the role of dark matter. The number-changing $3\to 2$ process, which sets the dark matter relic abundance, arises from the Wess-Zumino-Witten term. The theories give an explicit relationship between the $3\to 2$ annihilation rate and the $2\to 2$ self-scattering rate, which alters predictions for structure formation. This is a simple calculable realization of the strongly interacting massive-particle mechanism.

Figure 1

Solid curves: the solution to the Boltzmann equation of the $3\to 2$ system, yielding the measured dark matter relic abundance for the pions, $m_{\pi }/f_{\pi }$, as a function of the pion mass (left axis). Dashed curves: the self-scattering cross section along the solution to the Boltzmann equation, ${\sigma }_{\text{scatter}}/m_{\pi }$, as a function of the pion mass (right axis). All curves are for selected values of $N_c$ and $N_f$, for an $\mathrm{Sp}(N_c)$ gauge group with a conserved (left panel) or broken (right panel) $\mathrm{Sp}(2N_f)$ flavor symmetry. The solid horizontal line depicts the perturbative limit of $m_{\pi }/f_{\pi }\lesssim 2\pi$, providing a rough upper limit on the pion mass; the dashed horizontal line depicts the bullet-cluster and halo shape constraints on the self-scattering cross section (16), placing a rough lower limit on the pion mass. Each shaded region depicts the resulting approximate range for $m_{\pi }$ for the corresponding symmetry structure.